CS 15 - 859 : Algorithms for Big Data Fall 2017 Lecture 10 — Nov

And recall that the INDEX model has the lower bound for deterministic communication complexity: CCδ(INDEX) ≥ I(M ;X|R) ≥ n(1−H(δ)), where R is the shared common random string. We need a lower bound when conditioning on R for our earlier Gap-Hamming lower bound, which was a reduction from INDEX using the shared common random string R. Definition. Given (X,Y ) ∼ μ, the μ-distributional communication complexity of a function f(X,Y ) over the distribution μ, denoted by Dμ(f), is the minimum cost of a protocol that gives the correct answer with probability at least 2/3.